Given a mathematical program with objective function, MaxZ$=x^2+y^2,$ and one constraint, $x+y1,$ along with nonnegativity constraints on the two decision variables $(x,y0).$

Which of the following statements are true?

The optimal solution occurs at $(x,y)=(0\mathrm{.}5,0\mathrm{.}5)$

None of the answers are correct.

This problem is a linear program.

$(x,y)=(1,1)$ is a feasible solution for this problem.

The feasible region is unbounded.